The optimal design of a mechanical replacement for the natural heart has yet to be achieved - in spite of more than 30 years of effort. Recent advances in computational fluid dynamics (CFD), numerical optimization methods, and high performance computing have made it possible for us to contemplate computer-based systems that will partially automate the design process. With this motivation, we propose to design a three-dimensional impeller-type rotary blood pump that mitigates the fluid dynamic flow features related to blood trauma, while simultaneously improving hydrodynamic performance. Our state-of-the-art CFD-based design procedure solves the stationary incompressible Navier-Stokes equations and incorporates some of the latest advances made in the computational aerodynamics area. These advances include: 1) discrete sensitivity analysis to directly couple CFD with numerical optimization techniques: 2) fully implicit CFD solution methodologies to yield a highly efficient design procedure; and 3) the use of Bezier-Bernstein surface representations to generate a great variety of physically realistic shapes with a small number of design variables. The CFD flow algorithm is based on a Galerkin finite element method. Available options for the efficient gradient-based numerical optimization technique include either a method of feasible directions or a sequential quadratic programming (SQP) technique.